Direct identification of Poisson’s ratio in conventional and auxetic materials using FEM-based modal inversion

Abstract

This study introduces a finite-element-based modal inversion approach for determining Poisson’s ratio directly from impulse excitation of vibration (IET) measurements. Rather than estimating Poisson’s ratio indirectly through Young’s and shear moduli, or relying on closed-form plate solutions that assume ideal boundary conditions, the method uses the ratio between torsional and flexural resonance frequencies measured on a point-supported square plate. Finite-element eigenfrequency analyses are carried out with explicit representation of wire supports and with transverse shear deformation, rotary inertia, and thickness effects taken into account. These simulations are used to build a calibration map that relates the measured frequency ratio to Poisson’s ratio across a broad elastic range, extending into negative values. A Gaussian Process surrogate is then employed to obtain a smooth, strictly monotonic forward relation, which allows stable numerical inversion and provides a basis for uncertainty estimation. Validation experiments on metals, ceramics, and glasses show that the Poisson’s ratios obtained using this framework are in close agreement with independent ultrasonic measurements. Notably, the method also captures negative Poisson’s ratio behavior in an auxetic metamaterial specimen, with all inferred values falling within the auxetic regime. A closer inspection of the modal strain-energy distributions indicates that the elevated shear-energy contribution of the torsional mode is responsible for the pronounced sensitivity of the frequency ratio to Poisson’s ratio. Overall, the results point to a practical, robust, and modulus-independent resonance-based route for evaluating Poisson’s ratio in both conventional solids and architected auxetic materials under realistic testing conditions.